Membership function

About: Membership function is a research topic. Over the lifetime, 15795 publications have been published within this topic receiving 418366 citations.

Uncertain Fuzzy Reasoning: A Case Study in Modelling Expert Decision Making

Abstract: This paper presents a case study in which the introduction of vagueness or uncertainty into the membership functions of a fuzzy system was investigated in order to model the variation exhibited by experts in a medical decision-making context. A conventional (type-1) fuzzy expert system had previously been developed to assess the health of infants immediately after birth by analysis of the biochemical status of blood taken from infants' umbilical cords. Variation in decision making was introduced into the fuzzy expert system by means of membership functions which altered in small, predetermined manners over time. Three types of variation in membership functions were investigated: i) variation in the centre points, ii) variation in the widths, and iii) the addition of "white noise". Different levels (amounts) of uniformly distributed random variation were investigated for each of these types. Monte Carlo simulations were carried out to propagate the variation through the inferencing process in order to determine distributions of the conclusions reached. Interval valued type-2 fuzzy systems were also implemented to investigate the boundaries of variability in decisions. The results obtained were compared to the experts' decisions in order to determine which type and size of membership function variability best matched the experts' variability. The novel reasoning technique introduced in this study is termed nonstationary fuzzy reasoning

Generating an interpretable family of fuzzy partitions from data

Abstract: In this paper, we propose a new method to construct fuzzy partitions from data. The procedure generates a hierarchy including best partitions of all sizes from n to two fuzzy sets. The maximum size n is determined according to the data distribution and corresponds to the finest resolution level. We use an ascending method for which a merging criterion is needed. This criterion is based on the definition of a special metric distance suitable for fuzzy partitioning, and the merging is done under semantic constraints. The distance we define does not handle the point coordinates, but directly their membership degrees to the fuzzy sets of the partition. This leads to the introduction of the notions of internal and external distances. The hierarchical fuzzy partitioning is carried independently over each dimension, and, to demonstrate the partition potential, they are used to build fuzzy inference system using a simple selection mechanism. Due to the merging technique, all the fuzzy sets in the various partitions are interpretable as linguistic labels. The tradeoff between accuracy and interpretability constitutes the most promising aspect in our approach. Well known data sets are investigated and the results are compared with those obtained by other authors using different techniques. The method is also applied to real world agricultural data, the results are analyzed and weighed against those achieved by other methods, such as fuzzy clustering or discriminant analysis.

Differential Equations With Fuzzy Parameters

Abstract: This paper is concerned with systems of ordinary differential equations with fuzzy parameters. Applying the Zadeh extension principle to the equations, we introduce the notions of fuzzy solutions and of componentwise fuzzy solutions. The fuzzy extension of the solution operator is shown to provide the unique fuzzy solution as well as the maximal componentwise fuzzy solution. A numerical algorithm based on monotonicity properties of membership functions is presented, together with a proof of convergence. In an interplay of interval analysis and possibility theory, these methods allow to process subjective information on the possible fluctuations of parameters in models involving ordinary differential equations. This is demonstrated in two engineering applications: a queueing model for earthwork and a model of oscillations of bell-towers.